Given the vector a = (SiNx, 2), B = (1, - cosx), and a is perpendicular to B, find the value of TaNx and Tan (x-card / 4) | Math enthusiast | Mathematical art

Given the vector a = (SiNx, 2), B = (1, - cosx), and a is perpendicular to B, find the value of TaNx and Tan (x-card / 4)

From a perpendicular to B, it can be seen that if the scalar product of vectors a and B is zero, there will be
SiNx * 1 + 2 * (- cosx) = 0 = > sinx-2cosx = 0, so TaNx = SiNx / cosx = 2;
According to tan (a + b) = (Tana + tanb) / (1-tanatanb), the
The expansion of Tan (x - π / 4) has Tan [x + (- π / 4)] = (tanx-1) / (1 + TaNx), and then we take TaNx into the above formula, we can get
tan(x-π/4）=1/3

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